AP Physics C: Mechanics FRQ Guide 2026 — Free Response Tips & Scoring

The AP Physics C: Mechanics free response section is worth 50% of your total score — 45 raw points across 3 questions in 45 minutes. Unlike AP Physics 1, these questions require calculus: expect to integrate, differentiate, and set up differential equations.

AP Physics C: Mechanics FRQ Format

The 3 FRQ Types in Mechanics

Type 1: Calculus-Based Kinematics / Dynamics

These problems give you a position, velocity, or force as a function of time and ask you to derive other quantities. The pattern:

• Given x(t) or v(t) → differentiate to find v or a
• Given a(t) or F(t) → integrate to find v(t) or x(t)
• Use separation of variables for differential equations (common in drag-force problems)
• Work = ∫F dx for variable forces

Type 2: Rotation Problems

Almost always include: calculating moment of inertia (possibly with parallel axis theorem), finding torque, applying Στ = Iα, and dealing with rolling without slipping (v = Rω).

• Set up: draw diagram, identify rotation axis, list forces with moment arms
• Angular impulse-momentum: ΔL = ∫τ dt or conservation of L when τ_net = 0
• Rolling without slipping: ALWAYS check if problem specifies this; if so, v_cm = Rω
• Total kinetic energy of rolling object: K = ½mv² + ½Iω²

Type 3: Oscillations and Gravitation

SHM problems usually require deriving the equation of motion (show that a = -ω²x), identifying ω, T, and amplitude. Gravitation problems often test Kepler's third law, orbital mechanics, and escape velocity using energy conservation.

How AP Physics C: Mechanics FRQs Are Scored

Writing Calculus-Based Derivations

This is what separates Physics C from Physics 1. Here's the standard method for earning full derivation credit:

Integration Template

1. State your starting equation: Write F = ma or the relevant principle
2. Set up the integral explicitly: ∫ dv = ∫ (F/m) dt (show the integral sign and limits or variables)
3. Evaluate with limits: Leave in terms of the given variables; plug in only what the problem asks
4. Write units with the final answer

Differential Equation Setup

For drag-force problems (F = -bv type):

• Write Newton's second law: m(dv/dt) = mg - bv
• Separate variables: m dv/(mg - bv) = dt
• Integrate both sides with limits
• Solve for v(t)

Graders award points at each of these steps — even if the final answer is wrong, partial credit is available.

Rotation & Oscillation FRQ Strategy

Rotation Checklist

• Draw the system and label all forces and their positions relative to rotation axis
• Calculate I — if needed, use I = I_cm + md² (parallel axis theorem; provided on formula sheet)
• Write Στ = Iα; also write ΣF = ma for the translational component separately
• For rolling: combine v = Rω with Newton's equations; angular momentum about contact point may simplify
• Check: is angular momentum conserved? If Στ_ext = 0, use ΔL = 0

SHM Derivation Template

To prove a system undergoes SHM, you must show that the restoring force is proportional to displacement (F = -kx form):

1. Identify the equilibrium position
2. Displace by small amount x; write Newton's second law
3. Show the result is: d²x/dt² = -(k/m)x or equivalent
4. Identify ω² = k/m → T = 2π/ω = 2π√(m/k)

Most Common Mistakes on Physics C: Mechanics FRQs

• Forgetting to integrate: Using kinematic equations (v = v₀ + at) when force is NOT constant — always check if you need calculus
• Sign errors in derivatives: dU/dx gives force magnitude; F = -dU/dx includes the minus sign. Missing the negative = wrong direction
• Rolling vs. sliding: Not using v = Rω when rolling without slipping; or using it when the problem doesn't specify rolling
• Parallel axis theorem: Forgetting the +md² term when the rotation axis doesn't pass through the center of mass
• Angular momentum vs. linear: Confusing L = Iω (rotation about fixed axis) with L = mvr (point particle)
• Missing units: Physics C graders require units on final numerical answers — missing them costs points
• Not defining variables: If you introduce a variable not in the problem, define it. Graders can't award credit for undefined symbols

Related Resources

• AP Physics C: Mechanics Score Calculator
• AP Physics C: Mechanics Practice Test — 30 Questions
• AP Physics C: Mechanics Formula Sheet
• AP Physics C: E&M FRQ Guide
• AP Physics 1 FRQ Guide

Related Resources

• AP Physics C: Mechanics Score Calculator
• AP Physics C: Mechanics Score Curve 2026
• AP Physics C: Mechanics Practice Test -- 30 Questions